# Harmonograph

54 Tables of PaTTerns Overtone and simple ratio harmonics are shown below and opposite, arranged in order of increasing dissonance down the page. Open phase drawings display their ratio as the number of loops counted across and down. To find the ratio of a rotary drawing, draw both forms, concurrent both circles in the same direction and contrary in opposite directions. Count the loops in each, add the two numbers together and divide the total by two. This gives the larger ratio number. Subtract this from the contrary total to give the lower ratio number. Rotary figures for the ratio ab will have ba loops when both circles are concurrent, and ab loops when they are contrary. The designs shown here were all made with equal amplitudes.